What Would be My Best Option for Connecting the Parts of this Mesh?
Merge is probably merging everything at the center of the selected edge's bounding box.

You could do it manually, just enable edge snap and move the edges from the glove into the fingers and hands.
After you are done, select these edges (maybe grow the selection with ctrl + first, just to be sure), and then remove doubles. 

Another way would be to select both edge loops, bridge them, then edge slide on the rings into the other and then remove doubles.